Vol. 9, No. 9, 2015

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Families of nearly ordinary Eisenstein series on unitary groups

Xin Wan

Appendix: Kai-Wen Lan

Vol. 9 (2015), No. 9, 1955–2054
Abstract

We use the doubling method to construct p-adic L-functions and families of nearly ordinary Klingen Eisenstein series from nearly ordinary cusp forms on unitary groups of signature (r,s) and Hecke characters, and prove the constant terms of these Eisenstein series are divisible by the p-adic L-function, following earlier constructions of Eischen, Harris, Li, Skinner and Urban. We also make preliminary computations for the Fourier–Jacobi coefficients of the Eisenstein series. This provides a framework to do Iwasawa theory for cusp forms on unitary groups.

Keywords
Iwasawa theory, ordinary, Klingen Eisenstein series, unitary groups, $p$-adic $L$-function
Mathematical Subject Classification 2010
Primary: 11R23
Milestones
Received: 12 February 2014
Revised: 27 June 2015
Accepted: 18 August 2015
Published: 4 November 2015
Authors
Xin Wan
Department of Mathematics
Columbia University
Room 509, MC 4406
2990 Broadway
New York, NY 10027
United States
Kai-Wen Lan
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
USA